Numerical Modeling of Soil Erosion with Three Wall Laws at the Soil-Water Interface

Hatim El Assad, Benaissa Kissi, Rhanim Hassan, Parron Vera Miguel Angel, Rubio Cintas Maria Dolores, Guemimi Chafik, Mariem Kacem-Boureau


In the area of civil engineering and especially hydraulic structures, we find multiple anomalies that weakens mechanical characteristics of dikes, one of the most common anomalies is erosion phenomenon specifically pipe flow erosion which causes major damage to dam structures. This phenomenon is caused by a hole which is the result of the high pressure of water that facilitate the soil migration between the two sides of the dam. It becomes only a question of time until the diameter of the hole expands and causes destruction of the dam structure. This problem pushed physicist to perform many tests to quantify erosion kinetics, one of the most used tests to have logical and trusted results is the HET (hole erosion test). Meanwhile there is not much research regarding the models that govern these types of tests. Objectives: In this paper we modeled the HET using modeling software based on the Navier Stokes equations, this model tackles also the singularity of the interface structure/water using wall laws for a flow turbulence. Methods/Analysis: The studied soil in this paper is a clay soil, clay soil has the property of containing water more than most other soils. Three wall laws were applied on the soil / water interface to calculate the erosion rate in order to avoid the rupture of such a structure. The modlisitation was made on the ANSYS software. Findings: In this work, two-dimensional modeling was carried of the contrast of the early models which is one-dimensional model, the first one had shown that the wall-shear stress which is not uniform along the whole wall. Then using the linear erosion law to predict the non-uniform erosion along the whole length. The previous study found that the wall laws have a significant impact on the wall-shear stress, which affects the erosion interface in the fluid/soil, particularly at the hole's extremes. Our experiment revealed that the degraded profile is not uniform.


Doi: 10.28991/cej-2021-03091742

Full Text: PDF


Piping; Erosion Rate; Wall Laws; Piping Erosion.


Foster, Mark, Robin Fell, and Matt Spannagle. “The Statistics of Embankment Dam Failures and Accidents.” Canadian Geotechnical Journal 37, no. 5 (October 1, 2000): 1000–1024. doi:10.1139/t00-030.

Lachouette, Damien, Frédéric Golay, and Stéphane Bonelli. “One-Dimensional Modeling of Piping Flow Erosion.” Comptes Rendus Mécanique 336, no. 9 (September 2008): 731–736. doi:10.1016/j.crme.2008.06.007.

Fjar, Erling, Rachel M. Holt, A. M. Raaen, and P. Horsrud. “Petroleum Related Rock Mechanics 2nd Edition.” Developments in Petroleum Science (2008). doi:10.1016/s0376-7361(07)x5300-7.

Bonelli, Stéphane, and Olivier Brivois. “The Scaling Law in the Hole Erosion Test with a Constant Pressure Drop.” International Journal for Numerical and Analytical Methods in Geomechanics 32, no. 13 (September 2008): 1573–1595. doi:10.1002/nag.683.

Bonelli, Stéphane, Olivier Brivois, Roland Borghi, and Nadia Benahmed. “On the Modelling of Piping Erosion.” Comptes Rendus Mécanique 334, no. 8–9 (August 2006): 555–559. doi:10.1016/j.crme.2006.07.003.

Benaissa, Kissi, Parron Vera Miguel Angel, Rubio Cintas Maria Dlolores, Dubujet Philippe, Khamlichi Abdellatif, Bezzazi Mohammed, and El Bakkali Larbi. “Predicting Initial Erosion during the Hole Erosion Test by Using Turbulent Flow CFD Simulation.” Applied Mathematical Modelling 36, no. 8 (August 2012): 3359–3370. doi:10.1016/j.apm.2011.04.036.

Bredberg, Jonas. "On the wall boundary condition for turbulence models." Chalmers University of Technology, Department of Thermo and Fluid Dynamics. Internal Report 00/4. G oteborg (2000): 8-16.

Launder, Brian Edward, and Dudley Brian Spalding. "Lectures in mathematical models of turbulence." (1972).

Manual, U. D. F. "ANSYS FLUENT 12.0." Theory Guide (2009).

Boroomand, Mohammad Reza, and Amirhossein Mohammadi. “Investigation of k-ε Turbulent Models and Their Effects on Offset Jet Flow Simulation.” Civil Engineering Journal 5, no. 1 (January 27, 2019): 127. doi:10.28991/cej-2019-03091231.

Wan, Chi Fai, and Robin Fell. "Investigation of rate of erosion of soils in embankment dams." Journal of geotechnical and geoenvironmental engineering 130, no. 4 (2004): 373-380. doi:10.1061/(ASCE)1090-0241(2004)130:4(373).

Kuwano, Reiko, Luisa Fernanda Santa Spitia, Mehdi Bedja, and Masahide Otsubo. “Change in Mechanical Behaviour of Gap-Graded Soil Subjected to Internal Erosion Observed in Triaxial Compression and Torsional Shear.” Geomechanics for Energy and the Environment 27 (September 2021): 100197. doi:10.1016/j.gete.2020.100197.

Zhang, Dong-Mei, Cheng-Peng Gao, and Zhen-Yu Yin. “CFD-DEM Modeling of Seepage Erosion around Shield Tunnels.” Tunnelling and Underground Space Technology 83 (January 2019): 60–72. doi:10.1016/j.tust.2018.09.017.

Bi, Jinfeng, Haitao Zhang, Xianqi Luo, Hui Shen, and Zhuomin Li. “Modeling of Internal Erosion Using Particle Size as an Extra Dimension.” Computers and Geotechnics 133 (May 2021): 104021. doi:10.1016/j.compgeo.2021.104021.

Zhang, Dong-Mei, Wei-Wei Du, Mao-Zhu Peng, Shi-Jin Feng, and Zi-Li Li. “Experimental and Numerical Study of Internal Erosion Around Submerged Defective Pipe.” Tunnelling and Underground Space Technology 97 (March 2020): 103256. doi:10.1016/j.tust.2019.103256.

Alghurabi, Ahmed, Mysara Mohyaldinn, Shiferaw Jufar, Obai Younis, Abdullah Abduljabbar, and Mohd Azuwan. “CFD Numerical Simulation of Standalone Sand Screen Erosion Due to Gas-Sand Flow.” Journal of Natural Gas Science and Engineering 85 (January 2021): 103706. doi:10.1016/j.jngse.2020.103706.

Yerro, Alba, Alexander Rohe, and Kenichi Soga. “Modelling Internal Erosion with the Material Point Method.” Procedia Engineering 175 (2017): 365–372. doi:10.1016/j.proeng.2017.01.048.

Ye, Zhi, and Huabei Liu. “Investigating the Relationship Between Erosion-Induced Structural Damage and Lining Displacement Parameters in Shield Tunnelling.” Computers and Geotechnics 133 (May 2021): 104041. doi:10.1016/j.compgeo.2021.104041.

Batista, Pedro V.G., Jessica Davies, Marx L.N. Silva, and John N. Quinton. “On the Evaluation of Soil Erosion Models: Are We Doing Enough?” Earth-Science Reviews 197 (October 2019): 102898. doi:10.1016/j.earscirev.2019.102898.

Nguyen, Thanh Trung, and Buddhima Indraratna. “The Energy Transformation of Internal Erosion Based on Fluid-Particle Coupling.” Computers and Geotechnics 121 (May 2020): 103475. doi:10.1016/j.compgeo.2020.103475.

Qian, Jian-Gu, Wei-Yi Li, Zhen-Yu Yin, and Yi Yang. “Influences of Buried Depth and Grain Size Distribution on Seepage Erosion in Granular Soils Around Tunnel by Coupled CFD-DEM Approach.” Transportation Geotechnics 29 (July 2021): 100574. doi:10.1016/j.trgeo.2021.100574.

El-Din Fawzy, Hossam, Ali M. Basha, and Marco N. Botross. “Estimating a Mathematical Formula of Soil Erosion Under the Effect of Rainfall Simulation by Digital Close Range Photogrammetry Technique.” Alexandria Engineering Journal 59, no. 6 (December 2020): 5079–5097. doi:10.1016/j.aej.2020.09.039.

Hu, Feinan, Jingfang Liu, Chenyang Xu, Zilong Wang, Gang Liu, Hang Li, and Shiwei Zhao. “Soil Internal Forces Initiate Aggregate Breakdown and Splash Erosion.” Geoderma 320 (June 2018): 43–51. doi:10.1016/j.geoderma.2018.01.019.

Lei, Xiaoqin, Siming He, Xiaoqing Chen, Henry Wong, Lizhou Wu, and Enlong Liu. “A Generalized Interpolation Material Point Method for Modelling Coupled Seepage-Erosion-Deformation Process within Unsaturated Soils.” Advances in Water Resources 141 (July 2020): 103578. doi:10.1016/j.advwatres.2020.103578.

Li, Pengfei, Xingmin Mu, Joseph Holden, Yiping Wu, Brian Irvine, Fei Wang, Peng Gao, Guangju Zhao, and Wenyi Sun. “Comparison of Soil Erosion Models Used to Study the Chinese Loess Plateau.” Earth-Science Reviews 170 (July 2017): 17–30. doi:10.1016/j.earscirev.2017.05.005.

Sato, Mari, and Reiko Kuwano. “Laboratory Testing for Evaluation of the Influence of a Small Degree of Internal Erosion on Deformation and Stiffness.” Soils and Foundations 58, no. 3 (June 2018): 547–562. doi:10.1016/j.sandf.2018.01.004.

Wei, Yuan, Mei-li Zhan, Qing-fu Huang, Jin-chang Sheng, Yulong Luo, and Qing Zhou. “Erosion Probability Model of Base-Soil Particle Migration into a Granular Filter Under Local Flow.” International Journal of Sediment Research 34, no. 5 (October 2019): 455–460. doi:10.1016/j.ijsrc.2018.11.006.

Full Text: PDF

DOI: 10.28991/cej-2021-03091742


  • There are currently no refbacks.

Copyright (c) 2021 KISSI BENAISSA

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.